Heat Capacity in the Normal and Superconducting States and Critical Field of Niobium

Abstract

The heat capacity of a vacuum-annealed sample of niobium has been determined in the temperature range 1.5 to 30\ifmmode^\circ\else\textdegree\fi{}K. The heat capacity measurements in the normal state below the transition temperature were carried out in magnetic fields up to 4130 gauss. The effect of vacuum annealing on the heat capacity, transition temperature, and critical field was determined in an effort to obtain a so-called superconductor. After the initial annealing, within experimental error, the heat capacity in the superconducting state was found to be independent of further treatment. In the normal state the heat capacity (${C}_{n}$) can be represented by the relation ${C}_{n}=0.0018T+464.4{(\frac{T}{\ensuremath{\theta}})}^{3},$ where $\ensuremath{\theta}$ varies from 256 to 320 degrees depending on the temperature for the best annealed sample. No simple relationship holds for the heat capacity in the superconducting state. The heat capacity data could not be fitted to any existing corresponding state theory for superconductors.The zero-field transition temperature (${T}_{c}$) and the critical field (${H}_{c}$) were found to depend on the extent of annealing. For ${T}_{c}=9.07\ifmmode^\circ\else\textdegree\fi{}$K, ${(\frac{d{H}_{c}}{\mathrm{dT}})}_{T={T}_{c}}=1148$ gauss ${\mathrm{deg}}^{\ensuremath{-}1}$ whereas for ${T}_{c}=9.17\ifmmode^\circ\else\textdegree\fi{}$K, the highest transition temperature measured, ${(\frac{d{H}_{c}}{\mathrm{dT}})}_{T={T}_{c}}=734$ gauss ${\mathrm{deg}}^{\ensuremath{-}1}$. From the heat capacity data $(\frac{d{H}_{c}}{\mathrm{dT}})T={T}_{c}=415$ gauss ${\mathrm{deg}}^{\ensuremath{-}1}$ and ${H}_{0}$, the critical field at absolute zero=1944 gauss. It was not possible by vacuum annealing even at 2100\ifmmode^\circ\else\textdegree\fi{}C to obtain an ideal superconductor.